where \(b=1\)  or \(b = \infty \) , and identified two families of orthogonal polynomials that are eigenfunctions of
a differential operator, the Laguerre polynomials on the cone with \(b = +\infty \)  and the Jacobi polynomials on
the cone with \(b=1\) , and also established that the Jacobi family possesses an addition formula, which allows
us to carry out a preliminary study of the Fourier orthogonal series on the surface of the cone. Moreover,
analogous results were also established on the domain bounded by the surface of the cone, together with the
hyperplane \(t=1\)  when \(b=1\) . In [1]}, we considered the orthogonal structure on the surface of the
hyperboloid
\({\mathbb {V}}_0^{d+1} = \left\lbrace (x,t): \Vert x\Vert ^2 = c^2 (t^2 - \varrho ^2),\, x\in {\mathbb {R}}^d, \, \varrho \le |t| \le b\right\rbrace ,\) 
